Questions tagged [permutations]

For questions related to permutations, which can be viewed as re-ordering a collection of objects.

The word permutation has several possible meanings, based on context. In combinatorics, a permutation is generally taken to be a sequence containing every element from a finite set exactly once. Permutations of a finite set can be thought of as exactly the ways in which the elements of the set can be ordered.

In group theory, a permutation of a (not necessarily finite) set $S$ is a bijection $\sigma : S \to S$. The set of all permutations of $S$ forms a group under composition, called the symmetric group on $S$.

Reference: Permutation.

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How to find or construct permutation group which right cosets has only one element

A right transversal is also known as a set of right coset representatives http://www.maplesoft.com/support/help/Maple/view.aspx?path=group/cosets if impossible, does it mean that is condition to search all groups in order to find a permutation group…
bolo
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What is the general formula for the number of pairs of distinct members from two sets?

I know if I have a set including $N$ members, the general formula for the number of distinct pairs of members is $$ N(N-1) $$ Now if I have two sets, $A$ and $B$, including $a$ and $b$ members respectively (with all of them different altogether),…
Wisdom
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How do I prove this statement about permutations contained in the centralizer?

I have given the following permutation $$\sigma=\left(\begin{array}{rrr} 1&2&3&4&5&6&7&8&9 \\ 4&5&6&7&8&9&1&2&3 \end{array}\right)$$ and $I_1=\{1,4,7\},I_2=\{2,5,8\}, I_3=\{3,6,9\}$. I just know that $\sigma(I_i)=I_i$ for all $i$. Now we have given…
user123234
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How many possible permutations are there of a pacman board.

I am working on a Pacman RL project and need to validate that there are a correct number of state permutations that I generated. My logic is as follows: There are 15 player positions, 15 ghost positions, 15 positions that can have/not have a pellet.…
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How many combinations can 2 different groups have

So for example if we had A B and C and 1, 2 and 3 how many different group of 3 Letter/Number pairs can we make with no repetition as in, A1 B1 C1 A1 B1 C2 A1 B1 C3 A1 B2 C1 etc… By simply doing it I know the answer is 27 but I wonder if there is a…
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Divide objects into parts

I want to divide x distinct objects in some specified groups.. Lets say 3 groups of a,b,c number of I am able to find when objects are similar but not in this case.
user82699
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Where do I go from here on permutations of a password?

Password must be 5 characters of lowercase letters and digits. Must contain at least two letters and at least one digit with no repetition of digits. I have so far: $$ 26^2 + 10 \cdot 9 \cdot 8 $$ plus $$ 26^3 + 10 \cdot 9 $$ plus $$ 26^4 + 10 $$ Am…
toby843
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How many different arrangements are there of the word CARBON which end in a vowel?

All I can remember is to work out $6!$ then deal with the last term which can only be A or O but I do not know what to do! Can anyone please show me with workings and terminology? Thanks in advance!
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How many different combination we can construct?

The poster in McDonald’s says you can make a happy meal by choosing a main, a side and a drink. These are the choices: Main: Hamburger, Cheeseburger, Chicken Nuggets, Crispy Snack Wrap, Seared Snack Wrap Side: Fries, Apple pieces Drink: Soft drink,…
Peter
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Name for permutations that have to follow a certain order?

Is there a name for permutations that have to follow a certain order? For example, suppose ABC is a set of characters, and you are trying to figure out all the possible permutations, except, in every instance, A must be ordered before B. So…
Matt
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How many 8 digit even numbers greater than 40,000,000 can be formed using all the digits: 2,3,3,4,7,7,7,9

So what I’ve currently done is break it down into the following ends: 4_______2 4_______4 And etc, creating endings that would fit the question in asking for numbers that are both larger, and even. But I’m not sure how to proceed with the rest? Is…
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Permutation multiplication in S3

I have a question regarding multiplication in S3 with a=(2 3) and b=(1 2) The video I watched was showing left and right cosets in this case being different with ab=(1 3 2) ba=(1 2 3) I understand ba as (1 2)(2 3)= (1↦2↦3) but im not sure of ab as…
DDDDOO
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Number of ways to partition a $280$-character message into three non-empty segments

A monkey types a 280-character message on Twitter, using only the 26 upper-case English letters. A research assistant is trying to determine if there is any hidden meaning in the message, and tries partitioning the message into 3 segments (the…
Math Whiz
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Strictly nondecreasing permutations of numbers

Suppose I have a 6 digit lock that accepts 0-9 as inputs for the 6 slots. And I was told that the numbers in order from left to right are never less than the number to their left. so 0,0,0,0,0,0 would be valid but 0,1,2,3,2,9 would not. I tried to…
Wombles
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What is the number of permutations of N values or less in N space

Given a number N what is the number of Permutations in a Space of size N, of these N values. Example: N=2 $${P} = \{ (0,0,0), (0,0,1),(0,1,0),(1,0,0),(1,0,1),(1,1,0),(0,1,2),(1,0,2),(0,2,1),(1,2,0),(2,0,1),(2,1,0)\}$$ The restrictions to this…
Control
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